Energy Systems

, Volume 10, Issue 1, pp 95–112 | Cite as

A novel incentive-based demand response model for Cournot competition in electricity markets

  • José VuelvasEmail author
  • Fredy Ruiz
Original Paper


This paper presents an analysis of competition between generators when incentive-based demand response is employed in an electricity market. Thermal and hydropower generation are considered in the model. A smooth inverse demand function is designed using a sigmoid and two linear functions for modeling the consumer preferences under incentive-based demand response program. Generators compete to sell energy bilaterally to consumers and system operator provides transmission and arbitrage services. The profit of each agent is posed as an optimization problem, then the competition result is found by solving simultaneously Karush– Kuhn–Tucker conditions for all generators. A Nash–Cournot equilibrium is found when the system operates normally and at peak demand times when DR is required. Under this model, results show that DR diminishes the energy consumption at peak periods, shifts the power requirement to off-peak times and improves the net consumer surplus due to incentives received for participating in DR program. However, the generators decrease their profit due to the reduction of traded energy and market prices.


Incentive-based demand response Game theory Cournot equilibrium 



J. Vuelvas received a doctoral scholarship from COLCIENCIAS (Call 647-2014). This work has been partially supported by COLCIENCIAS (Grant 1203-669-4538, Acceso Universal a la Electricidad) and by Pontificia Universidad Javeriana (Grant ID 006486).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de ElectrónicaPontificia Universidad JaverianaBogotáColombia

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